Operations of Points on Elliptic Curve in Affine Coordinates
نویسندگان
چکیده
منابع مشابه
Operations of Points on Elliptic Curve in Projective Coordinates
In this article, we formalize operations of points on an elliptic curve over GF(p). Elliptic curve cryptography [7], whose security is based on a difficulty of discrete logarithm problem of elliptic curves, is important for information security. We prove that the two operations of points: compell ProjCo and addell ProjCo are unary and binary operations of a point over the elliptic curve. The te...
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For simplicity, we use the following convention: x is a set, i, j are integers, n, n1, n2 are natural numbers, and K, K1, K2 are fields. Let K be a field. A field is called a subfield of K if it satisfies the conditions (Def. 1). (Def. 1)(i) The carrier of it ⊆ the carrier of K, (ii) the addition of it = (the addition of K) (the carrier of it), (iii) the multiplication of it = (the multiplicati...
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Elliptic curve cryptosystems (ECC) are new generations of public key cryptosystems that have a smaller key size for the same level of security. The exponentiation on elliptic curve is the most important operation in ECC, so when the ECC is put into practice, the major problem is how to enhance the speed of the exponentiation. It is thus of great interest to develop algorithms for exponentiation...
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Elliptic curve cryptosystems, proposed by Koblitz ((11]) and Miller ((15]), can be constructed over a smaller eld of deenition than the ElGamal cryptosystems ((5]) or the RSA cryptosystems ((19]). This is why elliptic curve cryptosystems have begun to attract notice. In this paper, we investigate eecient elliptic curve exponentiation. We propose a new coordinate system and a new mixed coordinat...
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Elliptic curve cryptosystems, proposed by Koblitz ((12]) and Miller ((16]), can be constructed over a smaller eld of deenition than the ElGamal cryptosystems ((6]) or the RSA cryptosystems ((20]). This is why elliptic curve cryptosystems have begun to attract notice. In this paper, we investigate eecient elliptic curve exponentiation. We propose a new coordinate system and a new mixed coordinat...
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ژورنال
عنوان ژورنال: Formalized Mathematics
سال: 2019
ISSN: 1898-9934,1426-2630
DOI: 10.2478/forma-2019-0026